Amazon is facing mounting consumer backlash over its use of delivery company Yodel, with shoppers complaining of missing and damaged goods and orders that never turn up.

In the past week alone more than 100 people have joined about 5,000 others who have posted messages in Amazon's online forums calling for the online retailing giant to stop using the parcel delivery company. Some of these have also taken to Twitter to vent their anger, while yet more have posted tales of woe on Facebook.

Yodel is one of a number of delivery companies used by Amazon, and it also has contracts with other major retailers including Tesco, Argos and Boots. It has faced customer criticism since it bought DHL in January 2010, when it was known as Home Delivery Network Limited (HDNL). In an attempt to change its image it was rebranded later that year as Yodel, but the complaints have continued.

"We ordered a bicycle a week ago for our son Ted's third birthday," Amazon customer James Mossman said, who complained to the company on Twitter this week. "We ordered it in good time for his birthday and two days before his big day I came home to find a card from Yodel that had been put through the door with a delivery time on it and nothing else."

"After about 15 minutes on hold to Yodel they eventually traced my parcel and said it would be with me the next day. It wasn't. We called again and were told it would be Thursday at the earliest, the day after Ted's birthday, and that they had no record of the previous conversation. In the end we went out and bought another bike."

Amazon is one of the largest online retailers to use Yodel, but customer complaints about the delivery service are affecting the reputation of major businesses across the country.

In the past few weeks two major retailers, Mothercare and Matalan, have stopped using Yodel; John Lewis did the same at the end of 2011. Both Mothercare and Matalan declined to comment on the reasons for their decision.

Complaints about Yodel include inaccurate tracking information that has meant customers have no idea where their goods are for days or even weeks at a time; poor customer service and phone calls and emails that go unanswered; and goods being left in the rain and in other unsuitable places, including next to rubbish bins.

"I ordered eight shirts from Hawes & Curtis at £180," said Joe Goldberg, a London based Labour councillor and brand consultant. "I was told by Yodel that they would be delivered on Friday, but when I got home there was no card. On their website it said they were 'Delivered – as instructed'."

It wasn't until the following Wednesday, after Goldberg had contacted the delivery company on Twitter, that Rachel from Yodel came back with the following response:

"Hi Joe. I am not best pleased to have to tell you that unfortunately the driver has explained that your parcel was left in a bush, which was covered with bins. This I know is not an acceptable method of delivery to which we have raised this incident with the driver's manager. Would you be so kind as to inform me if your parcel is present in the location that the driver has described?"

Goldberg is still without his shirts. "My bin collection day is on Friday so I rather expect they are with the binmen," he said.

Yodel said it offers retailers a choice of signed for or leave safe delivery, and it has strict guidelines as to what constitutes a suitable safe place. It said it was working with clients to capture each customer's preferred delivery point.

One Amazon shareholder told the Guardian he was so concerned about the situation he recently wrote to the companies' investor relations department in America.

"Though not personally a victim of Yodel I was concerned by Amazon's apparently cavalier attitude," he said. "I think it is absolutely appalling that Amazon portrays itself as a caring company with good customer service but is just ignoring all these posts on its own website."

He had a response from Amazon UK that was the same as the one the company has subsequently given to the Guardian. "We work with a variety of carriers to deliver the many millions of orders that we dispatch on a weekly basis.

"Amazon measures itself on its ability to deliver items by the estimated delivery date we provide customers and the delivery performance is very strong. We take all customer feedback on board, actively monitor the performance of our carriers and make improvements in order that we can provide an even better service in the future."

Yodel is the biggest delivery service in the country outside of Royal Mail, delivering 170m parcels a year. Its director of marketing, Adam Smith, said this had to be considered when looking a the number of complaints it receives. "I think it is regretful that consumers feel like [they do] and we take that very seriously," he said.

The company had learned lessons from problems it had with deliveries in the build-up to the Christmas period in 2011, he said: "We have now put in place an extensive training programme for our drivers and are making sure every one of them has a handheld device that make it easier for us to track packages."

He added that the company was also in the process of making it easier for householders to track their parcels, and had made its customer service contact number free of charge following complaints about the amount it costs to call.

"We are listening to what we hear from individual cases and using that to inform our wider work as a business," Smith said. "We recognise we need to improve and have made some significant changes."